二维广义非线性Sine-Gordon方程的一个ADI格式

An ADI Scheme for the Generalized Nonlinear Sine-Gordon Equation in Two Dimensions

本文对二维广义非线性Sine-Gordon方程提出了一个带参数的ADI格式,其精度为O(τ2+h1),有效的降低了计算量,并证明了格式的稳定性与收敛性,最后通过参数的不同选取给出了数值算例,结果表明本文的格式是有效的和可靠的.

An ADI scheme with its truncation error is studied in this paper. By introduce two parameters, we can get better numerical results through choose different parameters with preserve its truncation error.The convergence and stability are obtained by the discrete functions analysis method. At last, we give the numerical results of the scheme.